Question

Use a 5 percent discount rate to compute the NPV of each of the following series of cash receipts and payments: Use Appendix A and Appendix B. $6,200 received now (year 0), $1,890 paid in year 3, and $4,000 paid in year 5. $10,000 paid now (year 0), $12,690 paid in year 2, and $31,000 received in year 8. $20,000 received now (year 0), $13,500 paid in year 5, and $7,500 paid in year 10.

Answer 1

Answer 1)

Calculation of Net Present Value

$ 6,200 received now (year 0), $ 1,890 paid in year 3, and $ 4,000 paid in year 5

NPV = Present value of cash inflows – present value of cash outflow

         = $ 6,200 - $ 4,767

         = $ 1,433

Therefore the NPV is $ 1,433.

Working Note:

Calculation of present value of cash Inflow:

Since the amount is received now (year 0), its present value will be equal to the amount received (i.e. $ 6,200)

Calculation of present value of cash Outflow:

Present value of cash Outflow = (Cash Outflow in Year 3 X Present value of $ 1 at 5% at the end of year 3) + (Cash Outflow in Year 5 X Present value of $ 1 at 5% at the end of year 5)

                                                       = ($ 1,890 X 0.86384) + ($ 4,000 X 0.78353)

                                                       = $ 1,632.66 + $ 3,134.12

                                                       = $ 4,766.78 or $ 4,767 (rounded off)

Answer 2)

Calculation of Net Present Value

$ 10,000 paid now (year 0), $ 12,690 paid in year 2 and $ 31,000 received in year 8

NPV = Present value of cash inflows – present value of cash outflow

         = $ 20,982 - $ 21,510

         = - $ 528

Therefore the NPV is - $ 528.

Working Note:

Calculation of present value of cash Inflow:

Present value of cash Inflow = (Cash Inflow in Year 8 X Present value of $ 1 at 5% at the end of year 8)

                                                       = ($ 31,000 X 0.67684)

                                                       = $ 20,982

Calculation of present value of cash Outflow:

Present value of cash Outflow = Cash Outflow in Year 0 + (Cash Outflow in Year 2 X Present value of $ 1 at 5% at the end of year 2)

                                                       = $ 10,000 + ($ 12,690 X 0.90703)

                                                       = $ 10,000 + $ 11,510

                                                       = $ 21,510

Answer 3)

Calculation of Net Present Value

$ 20,000 received now (year 0), $ 13,500 paid in year 5, and $ 7,500 paid in year 10

NPV = Present value of cash inflows – present value of cash outflow

         = $ 20,000 - $ 15,181

         = $ 4,819

Therefore the NPV is $ 4,819

Working Note:

Calculation of present value of cash Inflow:

Since the amount is received now (year 0), its present value will be equal to the amount received (i.e. $ 20,000)

Calculation of present value of cash Outflow:

Present value of cash Outflow = (Cash Outflow in Year 5 X Present value of $ 1 at 5% at the end of year 5) + (Cash Outflow in Year 10 X Present value of $ 1 at 5% at the end of year 10)

                                                       = ($ 13,500 X 0.78353) + ($ 7,500 X 0.61391)

                                                       = $ 10,577.66 + $ 4,604.33

                                                       = $ 15,181 (rounded off)